Radar system and method for determining a target point on a projectile trajectory



y 1965 c. R. CLEMENCE ETAL 3,182,316

RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1963 13 Sheets-Sheet l May 4, 1965 c. R.CLEMENCE ETAL 3,182,316

I RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1963 15 Sheets-Sheet 2 May 4; 1965 c. R.CLEMENCE ETAL 3,182,316

RADAR SYSTEM AND METHQD FOR DETERMINING A TARGET POINT 0" A PRQJECTILETRAJECTORY v zlvveAlTams CHARM-is 1?. Glen we;

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RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1963 15 Sheets-Sheet 5 May 4, 1965 C. R.CLEMENCE ETAL RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ONA PROJECTILE TRAJECTORY Filed April 1, 1963 13 Sheets-Sheet 7 ll lewrofs CW/MLas KICCFHEUGF Evf/ F I. lab/41 0 4/ WILL/6M C". Beau/M y 4,1965 are. CLEMENCE ETAL 3,182,316

RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1963' 13 Sheets-Sheet 8 May 4, 965 R. CLEMENCEETAL 3,182,316

RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1965 15 Sheets-Sheet 9 F7 L M y 4, 1965 c. R.CLEMENCE ETAL 3,182,316

RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1963 15 Sheets-Sheet 10 me" {44/5 "M9 241 547J z fl:

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RADAR SYS'I EM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJEGTORY Filed April 1, 1963 15 Sheets-Sheet 11 PPM May 4, 1965 c. R.CLEMENCE ETAL 3,132,316

RADAR SYSTEM AND METHOD FOR DETERMINING A TARGET POINT ON A PROJECTILETRAJECTORY Filed April 1, 1965 13 Sheets$heet 12 INVEA/Taflg C'mues R.Guam/c; 5 c Ev. flan/s04) W/zL/Aw 0. 81%

Arm 4 41 /5 CLEMENCE ETAL 3,182,316 RADAR SYSTEM AND METHOD FORDETERMINING A TARGET POINT ON A PROJECTILE TRAJECTORY 1s Sheets-Sheet 13May 4, 1965 Filed April 1, 1963 United States Patent C) 3,182,316 RADARSYSTEM AND METHOD FOR DETERMEN- ING A TARGET POINT ON A PROJEtJTlLETRAJECTORY Charles R. Clemeuce, Eric F. V. Robinson, and William C.Brown, Ottawa, Ontario, Canada, assignors to National Research Council,Ottawa, Ontario, Qanada, a body corporate Filed Apr. 1, 1963, Ser. No.269,233 Claims priority, appligagolrg Canada, Oct. 1, 1962,

3 a 8 (Ilaims. (Cl. 343-=-7) This invention relates to a radar systemand method, for use in locating enemy weapons by obtaining echoes fromthe projectiles fired by such weapons.

The invention is concerned with a radar system for determining at leasttwo points through which a projectile passes, the system including acomputer for determining the point of intersection of the trajectory ofthe projectile with the ground from two of such determined points. Whendesired for greater accuracy, the time interval required for passage ofthe projectile between said two points is inserted into the computer.Such a system is of particular utility when the weapon is hidden fromdirect visual or radar observation.

The radar system is equally useful for watching friendly projectilesaimed at the enemy weapon and for determining the points of impact orburst of such friendly projectiles by making the same extrapolation onthe trajectory of a falling projectile as for a rising projectile. Thepoint on the ground through which such trajectory extends (whether for arising or falling projectile) is called the target point. In the generalcase, the target point is the point of intersection of the projectiletrajectory with a selected plane referred to as the working plane. Theworking plane is defined as the one including the line between the radarsystem and the target point and all horizontal lines perpendicular tosaid line. The angle of the working plane will generally be chosen togive a ground location for the target point unless tactics otherwisedemand.

Such a system is described in W. C. Brown et al. United States patentapplication Serial No. 269,367 filed April 1, 1963. This applicationdescribes a system the antenna of which provides a narrow beamsubstantially circular in cross-section having a width of approximately16 mils (approximately 1, a mil being 360/6400) in both directions. Thesystem causes this narrow beam to scan horizontally throughapproximately 400 mils (22.5") alternately in two planes separated inangle by approximately 40 mils (2.25") at beam centers. This actiondefines, by the narrow beam locus, two vertically superposed, generallyhorizontal, fan-shaped beams, each scanned 20 times per second,hereinafter referred to as the upper and lower beams.

Echoes (intercepts) received from each of the upper and lower beams whena projectile passes through it, are displayed on a range-azimuth radardisplay in two series (one for each of said beams). The duty of theoperator is to observe or mark the center points of the leading edges ofthe first and last echoes received in each of the upper and lower beamsand to estimate and mark the mean points between each pair of these twoextreme center points. The radar screen is provided with an outersurface that can readily be marked by the operator using a suitablestylus. Having marked the mean center points on the screen, the operatorthen feeds in formation concerning the positions of these points into acomputer which calculates an extrapolated target point on the workingplane through which the projectile trajectory passes. The computerdisplays the position of this target point in counters as representingthe position of the Weapon. During the course of this operation, theoperator normally also determines AT, the time between the projectilebeing in similar positions in each of the upper and lower beams. Suchsimilar positions can conveniently be the moments when the projectileenters each of said beams.

The system outlined above was developed especially for observing enemymortar fire, or fire from other high angle weapons. It can similarly beused for watching friendly projectiles and calculating their point ofimpact or burst, but again the prime purpose of the system has beendirected to use with weapons having high angle trajectories.

Nevertheless, the system is inherently capable of detecting andcalculating low angle trajectories. Sometimes, however, the much largerditferences in range and/ or azimuth between the beam interceptsencountered with low angle trajectories are beyond the limits of thesystem, since system parameters have been selected to provide optimumresults with high angle trajectories. Often, if the echoes for one ofsaid upper and lower beams are on the screen, those for the other ofsaid beams will be wholly or partly beyond the edge of the screen. Ifthis occurs in the horizontal dimension of the screen, it means that theprojectile has a ditference in azimuth between beam intercepts almost asgreat or even greater than the length of the beam scan (400 mils in theexample). To make this value changeable at will, would be a complex andhence undesirable expedient. It would also reduce accuracy. In the rangedirection (vertically on the screen), the only way to avoid thedifiiculty of one series of echoes extending beyond the edge of thescreen, would be to vary the scale of the range sweep presented.However, this would bring all the echoes closer together and wouldgenerally reduce accuracy. Yet another problem posed by larger values ofAR and AA (the differences in range and azimuth between beamintercepts), is that of designing the computer to accept the largervalues. The computer must be built with some physical limits and thenarrower these can be made, the better will be the computer design fromthe viewpoint of accuracy and economy, provided satisfactory operationunder all normal conditions is assured. However, limits that aresatisfactory for computing high angle trajectories will often be toorestricted for computing low angle trajectories.

The operators inability to estimate properly the mean point ofinterception of the projectile trajectory with each of said beams mayarise from causes other than the low angle of the trajectory. He mayexperience adverse operating conditions such as signal fading orinterference. Such adverse conditions may prevent the proper display ofpart or all of the echoes of one or both beams.

The object of the present invention is to provide means for modifyingthe computer in a manner which will allow its use to be expanded tohandle low angle trajectories, or adverse conditions, such means to beused in conjunction with a modified operators procedure designed totolerate partial disappearance from the screen of one or more echoes ofone or other or both of said beams, or even total disappearance of theechoes of one beam. A further object is to achieve this end withoutexpanding the basic physical limits of the computer and hence withoutsacrifice to the accuracy attainable during operation under normalconditions (a high angle trajectory and all echoes visible).

This object is achieved by the provision of a radar system comprising(a) Means for emitting two closely vertically superposed, mutuallydivergent, generally horizontal, efiectively continuous, upper and lowerradar beams,

(b) Means for displaying echoes returned by a projectile travelling in atrajectory intersecting said upper and lower beams for derivation of atleast two points of the group comprising (i) A point on the echoreceived from the lower edge of the lower beam,

(ii) The corresponding point on the echo received from the upper edge ofthe lower beam,

(iii) The corresponding point on the echo received from the lower edgeof the upper beam,

(iv) The corresponding point on the echo received from the upper edge ofthe upper beam,

(v) The mean point between points (i) and (ii),

(vi) The mean point between points (iii) and (iv), and

(vii) The mean point between the series of echoes received from thelower beam and the series of echoes received from the upper beam (whichmay be the mean of points (ii) and (iii), or the mean of points (v) and(vi), or the mean of points (i) and (iv),

Means for determining range and azimuth values of a selected two of saidpoints measured from the radar system in relation to a known azimuthdatum,

(d) A computer,

(e) Means for supplying the computer with said determined range andazimuth values and with the values of the angles each of said upper andlower beams makes with the horizontal and with the value of the angle aworking plane makes with the horizontal,

(f) Said computer including means for calculating from said valuessupplied to it at least approximately a target range value from theradar system of a target point on said working plane through which suchtrajectory extends and a target azimuth value from the radar system ofsaid target point in relation to said datum,

(g) And said computer further including switching means operable tomodify said calculating means in accordance with the combination of twopoints selected.

The invention also has a method aspect which may be defined broadly as amethod of locating a target point that is at the point of intersectionof a working plane and the trajectory of a projectile, comprising (a)Emitting from a radar system two closely vertically superposed, mutuallydivergent, generally horizontal, effectively continuous, upper and lowerradar beams to intersect said trajectory,

(b) Determining the angle (0) the center of the lower beam makes withthe horizontal, and the angle (a) between the centers of the upper andlower beams,

(c) Estimating the angle (4:) the line lying in the working plane andextending from the radar system to said target point makes with thehorizontal,

(d) Displaying on a range-azimuth radar display echoes returned by saidprojectile during intersection of said upper and lower beams,

(e) Deriving at least two points of the group of points (i) to (vii)defined above,

(1) Selecting a combination of any two of said derived points other thanthe combination of points (v) and (vi),

(g) And employing the differences in range and azimuth of the points soselected, together with the values of said angles, to solve theequations where Rm is the target range value of the target point fromthe radar system, a 7

Am is the target azimuth value or the target point 7 measured from theradar system in relation to a known AR is the difference in rangebetween said selected points,

AA is the difference in azimuth between said selected points, and

K": WK V where the vertical component of the angle subtended at theradar system by the two selected points A manner of carrying theinvention into practice is illustrated diagrammatically in theaccompanying drawings. The specific system illustrated is provided byway of example only, the broad scope of the invention being limited onlyby the appended claims. In these drawings FIGURE 1 is a generalperspective view of a radar system according to the invention inoperation,

FIGURE 2 is a first diagram of a typical projectile trajectory,

FIGURE 3 is a further diagram of another projectile trajectory,

FIGURE 4 is a plan view of the diagram of FIGURE 3, also showing theposition of the radar system,

FIGURE 5 is another diagram provided to illustrate the geometry of thecomputations,

FIGURE 6a is a plan view of the area scanned by the radar system,

FIGURE 6b demonstrates the manner of presenting such area of scan(FIGURE 6a) on a radar B-scope during a long range searching sweep,

FIGURE 6c shows a portion of the presentation of FIGURE 6b enlarged asit appears for a short range sweep,

FIGURE 7a is a simplified front view of a portion of the radar controlpanel illustrating diagrammatically the appearance of an echo of aprojectile on the screen,

FIGURE 7b is another View similar to FIGURE 7a, a

short time later in operation,

FIGURE 70 is yet another view similar to FIGURES 7a and 7b at a laterstage, 7

FIGURE 7d is another similar view at yet a later stage in the radarobservance of a projectile,

FIGURE 7e is a view similar to FIGURES 7a to d showing the marks made bythe operator after the projectile echoes have faded and the manner ofuse of a marker spot,

FIGURE 7] is a view similar to FIGURE 7e at a later FIGURE 8 is ageneral overall circuit for the radar,

system, 7

FIGURE 9 is a more detailed illustration of the portion of the circuitof FIGURE 8 principally concerned with calculating the range of thetarget point, 7

FIGURE 10 is a more detailed illustration of'theportion of the circuitof FIGURE 8 principally concerned with calculating the elevation of thetarget point and providing certain parameters to the range and azimuthportions,

FIGURE 11 is a more detailed illustration of another portion of thecircuit of FIGURE 8 principally concerned with calculating the az muthof the target point,

FIGURE 12 is a detailed illustnation of the portion of the circuitprovided to display the intormation in the most conveniently usableform,

FIGURE 13 is a detail of the computer circuit incorporating features ofthe present invention, and

FIGURE 14 is a modified circuit as an alternative to FIGURE 13.

Overall system (FIGURE 1) FIGURE 1 shows the radar system RD mounted ona vehicle V being used to observe the trajectory T of a projectile firedby a mortar positioned out of direct visual or radar range behind hillsH. The antenna system of the radar system RD provides a narrow beamsubstantially circular in cross-section having a width of approximately16 mils (approximately 1, a mil being 360/6400) in both directions. Thesystem causes this narrow beam to scan horizontally throughapproximately 400 mils (22.5 alternately in two planes P1 and P2separated in angle by approximately 40 mils (225) at beam centers. Thisaction defines, by the narrow beam locus, two vertically superposedfan-shaped beams, each scanned 20 times per econd, hereinafter referredto as the upper and lower beams. This effect is achieved by use of aPoster type scanner SC similar to that disclosed in Foster US. PatentNo. 2,832,936 issued April 29, 1958, and modified to provide a dual beamin a manner similar to that described in Mobile Radar Pinpoints EnemyMortar Positions, by M. S. Iaffee et al. Electronics September 18, 1959,page 34 et seq. The scanner SC is placed at the focus of asemi-parabolic cylinder RF which reflects two focused beams. The scannerSC and reflector RF are mounted as an assembly on an antenna platform APon the vehicle V, which platform is maintained horizontal at all times(see United States Patent application No. 269,363 filed April 1, 1963).The scanner-refiector assembly can be inclined relative to thishorizontal platform AP to alter the angle of sight of the beams as apair while maintaining constant their angular separation. The limits ofthis adjustment may for practical purposes be set at 212 mils (12) abovethe horizontal to 106 mils (6) below the horizontal, these angles beingbetween the horizontal and the lower beam plane P2. The antenna assemblycan be rotated to provide complete radar coverage throughout 6460 mils(360) in azimuth.

Mathematics of the computations to be made (FIGURES Before consideringthe detailed nature of the display which appears on the radar screen asa result of a projectile passing through the upper and lower beams, itis necessary to consider the mathematics of the problem, taking as afirst assumption that the echoes received from each beam can be resolvedinto a single point on the trajectory T of the projectile, the range andazimuth of which point thus becomes known. The angle of sight 0 of thelower beam to the horizontal is known by the setting applied to thescanner-reflector assembly by the operator. In practice, the operatorwill make this angle of sight as small as he may having regard to thelimitations of the terrain. He will normally aim the antenna so that thelower beam just clears the treetops, or other high point, such as theupper outline of the hills H in FIGURE 1. He may be provided with atelescope aligned with the lower beam to facilitate this setting.

FIGURE 2 shows two intercept points a and b on trajectory T determinedby the radar system RD at ranges R1 and R2 respectively, it beingassumed for simplicity in this first diagram that the trajectory T isdirected straight towards the radar system RD with no change in azimuthbetween points a and b. The angle of sight of the lower beam is shown as19, and the fixed angle between the two beams is designated 0:. Theangle represents the dilference between the horizontal plane H? throughthe radar system RD and the working plane WP which is the plane in whichboth the radar system RD and the target point lie. The target point willbe assumed to be occupied by an enemy mortar for the presentdescription. The mortar is in fact positioned at the point M which isthe extrapolation of the trajectory T from points a and b to the workingplane WP, assuming the trajectory to be substantially parabolic. Point Mwould be the position of the mortar if it were on the horizontal planeHP, and points 1 and f are the corresponding points on the horizontaland the working planes for a straight line extrapolation from points aand b.

It will be appreciated that the angles at which the radar system workingin practice will be very small compared with the angles actually shownin FIGURE 1. It is necessary to exaggerate the size of the angles inFIGURE 1 in order to have a workable diagram. With this point in mind itwill be appreciated that many of the approximations employed in thesubsequent calculations are in fact a good deal closer to being truethan would at first sight appear from FIGURE 1, by reason of the factthat such small angles are encountered in practice.

Consider first the straight line extrapolation back from points a and bto point 7. Since triangle bca is similar to triangle nef Now,remembering that the angles are small, the follow ing approximations canbe made.

a-Rl6 IJC-R204-R10L 0 and a being vpnessed in radians.

Thus

R10 ef XAR=KAR This function thus represents the correction for straightline extrapolation, Where s 0 r f==a constant times 6 and thus varieswith that angle.

As above indicated, the working plane WP is provided to take care of thesituation occurring when the position of the mortar M is above or belowthat of the radar system RD, e.g. at M. An estimated working plane isinitially assumed by the operator as a rough calculation from a contourmap, since he knows the general location of the mortar, and is latercorrected as required in a manner to be described below. The operatorsinitial estimate of the working plane angle 1) radians does not affectthe angle of sight 0 of the radars lower beam; it merely plays a part inthe calculations.

Taking the working plane WP into account ef' z ii- A KAR where K nowequals namely a constant times (5-f-q5).

The mortar range Rm has now been found as Rl-j-KAR FIGURE 2 assumes thatthe mortar is firing directly towards the radar system RD. FIGURES 3 and4 are A2 (FIGURES 3 and 4) are assumed to be the azimuth angles inradians from a convenient datum (such as North) of the detected points aand b.

As FIGURE 4 shows car s (A1A2)R=AA R, where R:R1=R2.

Also

ae-R0 and I bcwRoc where 0 and a have the meanings already ascribed tothem. Consequently ef-KAA R where =i l or m as before. The mortarazimuth Am has now been found as Al-l-KAA.

If the mortar is not firing directly towards the radar system RD or on aline perpendicular to it, but at some angle in between, the samediagrams will apply for the components, and in the general case therewill be both AR and AA factors for each trajectory. To visualize AR, thetrajectory and its intercepts may be visualized as projected on avertical plane (AR plane) passing through the radar system and mortar,and to visualize AA, a similar projection may be made on a plane (AAplane) at right angles to the radar-mortar line. In each case, thetrajectory will be fore-shortened by the cosine of the angle between thetrajectory plane and the plane on which the projection is made. Themotar is located on the ground in polar coordinates to a firstapproximation as Rl-j-KAR; Al-l-KAA. The computer can thus determine themortar position by storing the information R1 and A1, calculating AR andAA from information set in by the operator, and performing the necessarymultiplications and additions to obtain the desired result.

The foregoing calculations have been based on a straight lineextrapolation and will result in quantities KAR and KAA which are toogreat and tend to overshoot the actual mortar position, due primarily tothe parabolic nature of the actual trajectory T. In other Words, thecalculations approximately find point f instead of point M. Due to theassumption that the distance ac in FIG- URE 2 is equal to the difierencein range R1R2=AR (which assumption is not entirely true), the overshooterror arrived at by assuming a straight line extrapolation is somewhatreduced, at least as far as range is concerned. It is not reduced inazimuth since the assumption just mentioned forms no part of thegeometry of FIGURE 3. Indeed, at certain angles of sight and angles ofmortar fire, the point f (as calculated by using the multiplication KARas explained) can even lie between the mortar M and the radar system RDin FIGURE 2.

The distance Mf (or My) may be found in terms of the parameters of atypical parabolic trajectory with reference to FIGURE 5, Dx being thedirectrix of the parabola, and p being the semi-latus rectum.

For any parabola S 2ph.

Also V the velocity of the projectile in the x direction at point a, isequal to the distance travelled, x, di-

, vided by the time taken. The projectile is assumed to be subject togravity only, and the horizontal component of the velocity to beconstant.

Thus:

Squaring and dividing throughout by g, the gravitational constant, givesNow it is also known from the geometry of a parabola that the time takenfor a projectile to reach the vertex, i is given by the expression v h=/2gt When x=S and t=t which occurs at the vertex, from the combinationof the foregoing equations The ventical component Vya of the projectilevelocity at point a is given by the well known expression for aparabolic trajectory ya y) It now the equation S :2ph is expanded forany point on the parabola, it becomes =v p mm with the sign representingan imaginary case.

The distance L shown in FIGURE 5 is given by the geometry of the systemfrom the relationship and using the above expression for x gives If wenow substitute in this equation the expressions for V and V we get zvmva Now, in the AR plane,

T A T where AT is the time between intercepts.

Also x=KAR, where K is the corrected value of K to obtain the truemortar position.

Substituting, we get Since the variables V and V will not be found notat point a but at a point half-way between a and b (see FIGURES 2 to 4)the quantity K should read K+ /2.

The equation to be solved becomes then KAR =K' R +W R K -K zaR K: (-QTaking g=9.8 meters/sec. and

:40 mils=0.03925 radians This constant is used in conjunction with otherconstants of the mechanical gearing described below in determining thecorrection to be applied as a shaft rotation. In the AA plane (FIGURE 3)a similar procedure may be used.

RAA -YT ZaR AA the same as before.

This expression is also modified further to substitute K+ /2 for K tobecome so that we now have the same multiplier, K, for both AR and AA,as given by The reason for substituting K+' /2 for K is that K is thecorrected value of K which latter should really be for a point'rnid-waybetween a and b. This expression K or K+% corrected) It should beremembered that K and K are pure (dimensionless) numbers.

Examination of FIGURES 2 and 3 shows that some approximations were made.For example in FIGURE 3 (AA plane) In FIGURE 2 it is apparent that thegreater part of the error is due to the approximation ca=R1-R2=AR wherethe distance as is the actual AR and as tll/l ca=cl +ua The distance cucan be approximately determined by ordinary trigonometry as cu-a 0+g 1mwhere Rm is the range from the radar system RD to the mortar M.

This equation is derived from the fact that the distance bs is given bythe Well known expression bs=2R2 sin 5 Since the angle between the linebs and the line cb is equal to (I s then cuwbs sin (0+3) a a #2122 sin 5sin (ti-I Taking (1:40 mils, and Rm in meters, and 0 in mils,

this equation becomes Thus the true target (mortar) position in polarcoordinates from the radar system RD, where Am is the angle betweenNorth and the line of sight to the target, are given by equations andAm=A1+KAA (2) where 6 I 1 2 2 j1 +/2 T (3) These equations have beendesignated Equations 1, 2 and 3 respectively for ease of subsequentreference to them. It should be pointed out that, in applying the aboveequations, account must be taken of the sign of AA and AR. It AZ isclockwise from Al, AA is negative; and if the mortar is firing away fromthe radar, AR is negative.

The true target position has thus been determined in 11 plar coordinateRm and Am, and it remains only to convert to rectangular (Cartesian)coordinates. This is done by means of a resolver, the output of which isRm sine Am and Rm cosine Am If the radar position is added to thesequantities as Eastings and Northings then Rm sine Am-l-RadarEastings=Target Eastings Rm cosine Am-j-Radar Northings=Target NorthingsBesides determining the target position in plan, the computer willprovide an elevation (in feet above sea level) of this position. This isnecessary for the operator to determine the correct angle 5 of theworking plane WP. The elevation of the target relative to the radar isRm sine but for simplicity, and because 'is always small, this is takenas Rm. With being measured downwards from the horizontal, the equationfor elevation becomes Rm+Radar Elevation=Target Elevation The manner ofuse of this information by the operator is described below.

Nature of echo presentation and operators procedure (FIGURES 6 and 7)Attention is now directed to FIGURES 6a, b and 0. FIGURE 6a shows a planview of a typical sector SR scanned by the radar RD. Two composite echodisplays E and E produced by the lower and upper beams, respectively,are shown. FIGURE 6b demonstrates the manner in which the sector SR ispresented on the screen S of a B-scope, that is to say a scope whichexhibits azimuth along the horizontal axis and range along the verticalaxis. After having detected a weapon firing, the operator will enlargethe critical area of the sweep as demonstrated by FIGURE 6c.

The echo displays actually received in practice are more complex thanthose illustrated in FIGURES 6a, b and c, and attention is nowtransferred to FIGURES 7a to i for a more detailed discussion of thenature of the display on the screen actually observed by the operator.

As a projectile enters the field of scan of the lower beam, an echo E1is displayed on the screen S by a group of individual signal returnsresulting from a single passage of the narrow beam across theprojectile. The center of the leading (lower) edge of this echo (pointC1) rep resents the true position of the object (projectile) beingobserved. As the narrow beam continues to scan, a series of such echoesappears on the screen S. These echoes are indicated as E1 to E5 inFIGURE 7b and make up the composite echo E of FIGURES 6a to c. Inreality there may be many more than five individual echoes in this Hseries. Echoes E1 to E4 are shown in broken lines because some fadingwill have taken place by the time of the last echo E5 appears.Conditions permitting, the duty of the operator is to determine and markthe center points of the leading edges of the first and last echoes andto estimate and mark the mean point between these two extreme'centerpoints. The screen is provided with an outer surface that can readily bemarked by the operator using a suitable stylus. He marks points C1 andC5 'on the screen as echoes E1 and E5 appear, and later estimates andmarks the mean point CML. If he cannot conveniently mark the leadingedges, he marks the centers or the trailing edges, provided he alwaysuses corresponding points.

Assuming that the weapon is firing from left to right and towards theradar system RD, the second series of echoes UR detected by the upperbeam and shown as composite echo E in FIGURES 6a to 0 appears first asan echo E6 (FIGURE 70) and continues down to echo E10 (FIGURE 7d). Theseechoes of the second series will similarly have leading edge centerpoints C6 to C14),

12 the mean point of which is designated CMU. The upper beam echoes willappear in a lower position on the screen S than the lower beam echoeswhen the weapon is firing towards the radar, since the range will haveshortened somewhat by the time the projectile reaches the upper beam.

As well as carrying out the functions just described, the operator willtime the interval the projectile takes to pass from the lower to theupper beam. He can do this either by comparing the first echo of eachbeam, the last echo of each beam or theoretically any pair ofcorresponding points on the two beams. It has been assumed in FIG- URES7a to it that he uses the first method and records the time between therespective first echoes E1 and E6 of the lower and upper echo series LRand UR. For this purpose, the operator has a push button hand switch HSsituated beside the screen S. A right-handed operator will push theswitch HS with his left hand, to leave his right hand free for markingthe screen S. A second, parallel operating, hand switch HS is providedfor lefthanded operators. As FIGURE 7a indicates by an arrow, theoperator will push in the switch HS immediately on appearance of thefirst echo E1 of the lower beam LB.

'This operation will start the timer TM. When the first echo E6 of theupper beam UB appears (FIGURE 7c) the operator will again push the handswitch HS to stop timer TM which will now remain in its new positionindicating and simultaneously inserting into the computer AT, the timeof travel from the lower to the upper beam by the projectile.

The screen S is also provided with a marker spot MS, which is anelectronic marker produced by conventional circuitry in the radartransmitter-receiver combination' FS (FIGURE 7e). Depression of switchFS brings the' computer into full operation, as will appear in moredetail below. Although illustrated simply, the switch FS is a toggleswitch of the type commonly employed to raise and lower the headlightsof an automobile, that is to say a switch which remains in each acquiredposition until reactivated by a further depression of the operators footto be reversed. As demonstrated by FIGURE 7 after closing switch FS theoperator moves the marker spot MS with handwheels AMH and RMH to thepoint CMU, while switch FS remains closed. In this way, the operatorfeeds into the computer the difference in range AR and the difference inazimuth AA between these two points.

Consideration should now be given to FIGURES 7g, h and i whichillustrate typical conditions when the system is used to observe aprojectile with a low angle trajectory.

FIGURE 7g shows the conditions on screen S for a projectile with acomparatively low angle trajectory fired at a substantial angle to theradar upper and lower beams (to produce a large value of AA). Points C1,CML and C5 are on the screen, but of the upper series only point C6appears. Marks CMU and C10 in FIGURE 7g dem; onstrate where these pointswould have been displayed, if they had not been oif the screen. It mustbe remembered that the operator has to estimate points CML and CMUvisually, and to do this he must see the eirtreme points'on both sides.FIGURE 7g is merely one example of numerous possible variants of asituation in which all six points cannot be displayed, and in which, asa result,

one or both of the mean points CML, CMU cannot be properly determined.FIGURE 7h shows a different but related situation in l3 which, althoughall six points can be seen and hence the mean points CML, CMU can bedetermined, the range difference AR is greater than the computer canaccept by reason of its physical limits. A similar situation can arisein which the azimuth difference AA is greater than the computer canaccept by reason of its physical limits.

The present invention avoids these difficulties by providing formodification of the operators procedure described above and by providingmeans in the computer for taking the modified procedure into account,without any necessity to expand the physical limits of the computer andhence reduce its inherent accuracy which remains available when cratingconditions enable points CML and CMU to be used.

In accordance with the modified procedure, the operator followsbasically the same routine as above described, except that he uses adifferent pair of points, one or the other or both of points CML and CMUbeing either unavailable (FIGURE 7g), or unusable (FIGURE 71 orincapable of reasonably accurate estimation (for example by reason ofinterference with or fading of one or more of the beam edge points C1,C5, C6 and C18). He has a number of choices of the pair of points touse, and the choice he makes will depend on the radar display he hasavailable.

In addition to the six points Cl, CML, C5, C6, CMU and Cltl, a seventhpoint, the mean point CMM may be derived. This mean point CMM is themean point between the two series of echoes. In practice it can bederived by taking the mean point between points C5 and C6. This is thepreferred method. Alternatively, an accept-- able approximation can beobtained by taking the mean or" points CML and CMU, or the mean ofpoints Cl and C10.

With seven points potentially available, C1, CML, C5, CMM, C6, CMU andCltl there is a theoretical choice of twenty-one different combinationsof any two of these points, including the normal combination CML andCMU. There is further room for variation, in that, as indicated above,the center points or trailing edges can be used instead of the leadingedges of the echoes. However, if this is done, it must be applieduniformly by always using a pair of points which correspond to eachother in their position within the physical ilmits of the respectiveechoes. The total number of combinations available is thus unchanged.

The operator must always place the marker spot MS first on the lower oneof the two points chosen (that is lower in terms of the physicalinterception in space of beams and projectile-not necessarily lower onthe operators screen), before moving the spot MS to the second chosenpoint. In any practical situation only some of the twenty-onecombinations may be available to the operator. The four combinationsfrom which it is usually preferred to make a choice, when the normalcombination is unavailable, are described under the titles of split,lower, upper and doubler. For the split combination the operator takespoints C5 and C6. If one of the echo series is entirely absent from thescreen (say the upper series), the operator may take the first and lastpoints of the lower beam, points Cit and C5, which is the lowercombination. Analogously, the upper combination takes points C6 and Cliland feeds their mutual differences in range and azimuth into thecomputer.

As the fourth alternative, especially suited to the FIG-- URE 7hsituation, the operator uses point CMM together with the point CML tofeed the computer. This is the doubler combination, because the valuesof AR and AA fed into the computer are approximately halved and musttherefore be effectively doubled therein.

When such operator procedures are followed the computer is modified byswitching means described below in connection with FIGURES 13 and 14.Before deseribing these figures it will be necessary to describe FIG-URES 8t'o12.

M- Operation of the computer (FIGURES 8 to 12) For an understanding ofthe manner in which the target point is calculated from the informationavailable, reference will now be made to FIGURES 8 to 12.

FIGURE 8 shows as a single block RDR a radar transmitter and receiverassembly with related circuits for the B-scope and the electronic markerspot MS. These circuits are conventional and their particular natureforms no part of the present invention. Assembly RDR is coupledelectrically and mechanically to the antenna ANT comprising thescanner-reflector assembly already described.

The computer portion of the circuitry which the remainder of FIGURE 8illustrates in general layout can conveniently be roughly divided intoportions which deal respectively with range, elevation, azimuth andinformation display. These circuit portions are treated separately andin more detail in FIGURES 9, 10, 11 and 12 respectively. Although thesecircuits are interrelated sufficiently to require some reference to eachother in understanding, the description which follows will, as far aspossible, take each circuit separately and examine its composition andfunction. (In all these circuit dia grams, broken lines signifymechanical connection, full lines electrical connection.)

The range circuit portion (FIGURE 9) The range marker handwheel RMHpreviously described in connection with FIGURE 7 controls movement ofthe marker spot MS on the screen S in the range direction through agoniometer assembly G1 to which its rotation is transmitted by shaft H1.Goniometer assembly Gl controls the range position of the marker spot MSon the screen. It also, through shaft H4, operates a cam CAM7 whichcontrols a pulse repetition frequency switch PRFS. This switch changesover the radar system from short to long range.

At the same time the handwheel motion is transmitted by shaft Hi to afirst input of a mechanical differential 331. Thus, when the marker spotMS is moved to the point CML in FIGURE 7a, the range R1 of such point isfed into the differential Dl. As already explained, once the marker spotMS has been aligned with point CML, the operator operates foot switch FSwhich remains closed. As shown in FIGURE 9, foot switch PS serves toenergize a mechanical clutch CLZ which now connects the shaft Hi. of thehandwheel RMH to shaft H3 which forms another input to differential D1acting opposition to shaft Hi. As a result, when the marker spot MS ismoved by the operator towards point CMU (FEGURE 7 the output ofdifferential Dl, shaft H2, remains stationary since AR (the rangedifference between points CML and CMU) is being inserted twice inopposite senses into differential D1. The position of shaft H2represents the range value R1, while shaft H3 is moved a distance equalto -AR.

Foot switch FS energizes relay RY, one pair of con tacts RYl of which isopened to de-energize a clutch Cit which had hitherto been holding shaftH3 under the control of a motor Ml. Contacts RY2 which are ciosed byenergization of the relay RY serve to ground the input to a motor returnamplifier MR1 deenergizing m tor M1. The zeroing function of this motorMl will be described below in connection with the resetting of thesystem.

The factor -AR is transmitted by shaft H3 to a movable slider on aresistor RRZ. This part of the circuit is concerned with simulatingEquation 1 above, which for convenience is here repeated.

If the last term is called I, this equation becomes

1. A RADAR SYSTEM COMPRISING (A) MEANS FOR EMITTING TWO CLOSELYVERTICALLY SUPERPOSED, MUTUALLY DIVERGENT, GENERALLY HORIZONTAL,EFFECTIVELY CONTINUOUS, UPPER AND LOWER RADAR BEAMS, (B) MEANS FORDISPLAYING ECHOES RETURNED BY A PROJECTILE TRAVELLING IN A TRAJECTORYINTERSECTING SAID UPPER AND LOWER BEAMS FOR DERIVATION OF AT LEAST TWOPOINTS OF THE GROUP COMPRISING (I) A POINT ON THE ECHO RECEIVED FROM THELOWER EDGE OF THE LOWER BEAM, (II) THE CORRESPONDING POINT ON THE ECHORECEIVED FROM THE UPPER EDGE OF THE LOWER BEAM, (III) THE CORRESPONDINGPOINT ON THE ECHO RECEIVED FROM THE LOWER EDGE OF THE UPPER BEAM, (IV)THE CORRESPONDING POINT ON THE ECHO RECEIVED FROM THE UPPER EDGE OF THEUPPER BEAM, (V) THE MEAN POINT BETWEEN POINTS (I) AND (II), (VI) THEMEAN POINT BETWEEN POINTS (III) AND (IV), AND (VII) THE MEANS POINTBETWEEN THE SERIES OF ECHOES RECEIVED FROM THE LOWER BEAM AND THE SERIESOF ECHOES RECEIVED FROM THE UPPER BEAM, (C) MEANS FOR DETERMINING RANGEAND AZIMUTH VALUES OF A SELECTED TWO OF SAID POINTS MEASURED FROM THERADAR SYSTEM IN RELATION TO A KNOWN AZIMUTH DATUM, (D) A COMUPTER, (E)MEANS FOR SUPPLYING THE COMPUTER WITH SAID DETERMINED RANGE AND AZIMUTHVALUES AND WITH THE VALUES OF THE ANGLES EACH OF SAID UPPER AND LOWERBEAMS MAKES WITH THE HORIZONTAL AND WITH THE VALUE OF THE ANGLE AWORKING PLANE MAKES WITH THE HORIZONTAL, (F) SAID COMPUTER INCLUDINGMEANS FOR CALCULATING FROM SAID VALUES SUPPLIED TO IT AT LEASTAPPROXIMATELY A TARGET RANGE VALUE FROM THE RADAR SYSTEM OF A TARGETPOINT ON SAID WORKING PLANE THROUGH WHICH SUCH TRAJECTORY EXTENDS AND ATARGET AZIMUTH VALUE FROM THE RADAR SYSTEM OF SAID TARGET POINT INRELATION TO SAID DATUM, (G) AND SAID COMPUTER FURTHER INCLUDINGSWITCHING MEANS OPERABLE TO MODIFY SAID CALCULATING MEANS IN ACCORDANCEWITH THE COMBINATION OF TWO POINTS SELECTED.